For my 2 Cents, We stayed at Many Glacier Campground in Glacier NP and loved it. Primitive but beautiful with hiking near by. Wonderful mountain vistas from the CG and lots of Mountain Goats up in the high pastures (visible with Binoculars from the CG).
I would also highly recommend the scenic highway between Bozeman MT and West Yellowstone. One of the best drives in the west for my money.
FarticOx
FarcticOx
Run Silent, Run Deep
2003 F350 Diesel DRW.
2005 Arctic Fox B1150 solar powered dry camper.
We did a very similar trip last year at about the same time. We had no problems finding sites in the National Park campgrounds at Glacier or Grand Tetons. Yellowstone was a bit more crowded but we still found a good site. Be prepared for cold weather at this time of year.